Answer:
[tex](x-5)^{2} +(y+4)^{2} =10^{2}[/tex]
Step-by-step explanation:
To calculate the formula of a circle that is not in the center fo the graph, you need two things, the point where the cirlce is centered and any point in the circumference, and with this you can calculate the radius, to calculate the first part you just need the next formula:
[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]
Where [tex]x^{c}y^{c}[/tex] are the x and y where the center of the circle is, so you just evaluate with the values you are given:
[tex](x-x^{c})+(y-y^{c})=r^{2}[/tex]
[tex](x-(5))+(y-(-4))=r^{2}[/tex]
[tex](x-5)+(y+4)=r^{2}[/tex]
Now that you have the first part, we can calculate the radius, remember taht the radius of any given circumference in the graph is the hypotenuse of the X´s and Y´s that are part of those two points given, so we just calculate it like any hypotenuse:
[tex]c=\sqrt{x^{2}+ y^{2} }[/tex]
To calculate this we would rest to the point in the circumference, the center of the circumference, like this:
[tex]c=\sqrt{(x^{2}-x^{1})^{2}+ (y^{2}-y^{1})^{2} }[/tex]
[tex]c=\sqrt{(-3-5)^{2}+ (2-(-4))^{2} }[/tex]
[tex]c=\sqrt{(-8)^{2}+ (6)^{2} }[/tex]
[tex]c=\sqrt{64+ 36 }[/tex]
[tex]c=\sqrt{100 }[/tex]
[tex]c=10[/tex]
So your radius would be 10, now we just put that into our previous formula:
[tex](x-5)+(y+4)=r^{2}[/tex]
[tex](x-5)+(y+4)=10^{2}[/tex]
So the formula for the circle that is centered at (5,-4) and passes through the point (-3,2) would be:
[tex](x-5)+(y+4)=10^{2}[/tex]
Prism A is similar to Prism B with a scale factor of 6:5. If the volume of Prism B is 875 m2, find the volume of Prism A.
Answer:
[tex]\large\boxed{V_A=1512\ m^3}[/tex]
Step-by-step explanation:
[tex]\text{If a prism A is similar to a prism B with a scale k, then:}\\\\\text{1.\ The ratio of the lengths of the corresponding edges is equal to the scale k}\\\\\dfrac{a}{b}=k\\\\\text{2. The ratio of the surface area of the prisms is equal}\\\text{to the square of the scale k}\\\\\dfrac{S.A._A}{S.A._B}=k^2\\\\\text{3. The ratio of the prism volume is equal to the cube of the scale k}\\\\\dfrac{V_A}{V_B}=k^3[/tex]
[tex]\text{We have}\\\\k=6:5=\dfrac{6}{5}\\\\V_B=875\ m^3\\\\V_A=x\\\\\text{Substitute to 3.}\\\\\dfrac{x}{875}=\left(\dfrac{6}{5}\right)^3\\\\\dfrac{x}{875}=\dfrac{216}{125}\qquad\text{cross multiply}\\\\125x=(875)(216)\qquad\text{divide both sides by 125}\\\\x=\dfrac{(875)(216)}{125}\\\\x=\dfrac{(7)(216)}{1}\\\\x=1512\ m^3[/tex]
Prism A is similar to Prism B with a scale factor of 6:5. If the volume of Prism B is 875 m2. The volume of prism B is 1512 meter square.
How to calculate the scale factor?Suppose the initial measurement of a figure was x units.
And let the figure is scaled and the new measurement is of y units.
Since the scaling is done by multiplication of some constant, that constant is called the scale factor.
Let that constant be 's'.
Then we have:
[tex]s \times x = y\\s = \dfrac{y}{x}[/tex]
Thus, the scale factor is the ratio of the new measurement to the old measurement.
Prism A is similar to Prism B with a scale factor of 6:5.
If the volume of Prism B is 875 m2, find the volume of Prism A.
scale factor = 6/5
The ratio of the surface area of the prism A to the prism B
A1 / A2 = k^2
The ratio of the prism is equal to the cube of the scale k.
V1 / V2 = k^3
Let x be the volume of Prism A.
x / 875 = (6/5)^2
x / 875 = 216 / 125
x = 875 * 216 / 125
x = 1512
Therefore, the volume of prism B is 1512 meter square.
learn more on scale factors here:
brainly.com/question/14967117
#SPJ2
PLEASE IM GONNA FAIL 7TH GRADE
Selective breeding _____.
1. creates offspring which are genetically identical to the parent
2. is the process of breeding only organisms with desirable traits
3. involves the removal of the nucleus of a cell
4. combines traits from organisms of different species
Answer:
2. the process of breeding only organisms with desirable traits
Step-by-step explanation:
Answer:
the answer is the second one
Step-by-step explanation:
Which of the following statements best describes the location of a vertex on
a parabola?
A it's is located halfway between the parabolas focus and directrix
B it is located on the parabola directix
C it is located on the parabola focus
D it is located halfway between the parabola two foci
Answer:
A it's is located halfway between the parabolas focus and directrix
Step-by-step explanation:
hope this helps
Answer:
Option A is correct that is it's is located halfway between the parabolas focus and directrix.
Step-by-step explanation:
We are given a parabola.
To find: Best statement which describes the location of the vertex on the parabola.
Standard Equation of Parabola which open on the Right hand direction.
( y - k )² = 4a( x - h )
Here, ( h , k ) is the vertex of the parabola and ( h + a , k ) is the focus.
Distance of the focus from vertex = a
Equation of the Directrix of the Parabola is , y = k - a
Distance of the Directrix from vertex = a
Therefore, Option A is correct that is it's is located halfway between the parabolas focus and directrix.
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Match each set of vertices of quadrilateral EFGH with the transformation that shows it is congruent to ABCD.
E(-3, -4), F(1, -3), G(3, -6), and H(1, -6)
a translation 7 units right
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1)
a reflection across the y-axis
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6)
a reflection across the x-axis
E(4, 4), F(8, 3), G(10, 6), and H(8, 6)
a translation 5 units down
arrowBoth
arrowBoth
arrowBoth
arrowBoth
Reset Next
Previous3 Next Transformations and Congruence: Mastery Test Submit Test Tools Info
© 2019 Edmentum. All rights reserved.
E(-3, -4), F(1, -3), G(3, -6), and H(1, -6); a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1); a translation 5 units down
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6); a reflection across the y-axis
E(4, 4), F(8, 3), G(10, 6), and H(8, 6);a translation 7 units right
What is transformation?
Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Quadrilateral ABCD has vertices A(-3, 4), B(1, 3), C(3, 6), and D(1, 6). Hence:
E(-3, -4), F(1, -3), G(3, -6), and H(1, -6); a reflection across the x-axis
E(-3, -1), F(1, -2), G(3, 1), and H(1, 1); a translation 5 units down
E(3, 4), F(-1, 3), G(-3, 6), and H(-1, 6); a reflection across the y-axis
E(4, 4), F(8, 3), G(10, 6), and H(8, 6);a translation 7 units right
Find out more on transformation at: https://brainly.com/question/4289712
Finding Intercepts of Quadratic FunctionsConsider the function f(x) = x2 + 12x + 11.
x-intercepts:
0 = x2 + 12x + 11
0 = (x + 1)(x+ 11)
y-intercept:
f(0) = (0)2 + 12(0) + 11
What are the intercepts of the function?
The x-intercepts are .
The y-intercept is .
Answer:
x1=-11 x2=-1 y=11
Step-by-step explanation:
you can see the explanation in the pics
In physics, if a moving object has a starting position at so, an initial velocity of vo, and a constant acceleration a, the
the position S at any time t>O is given by:
S = 1/2 at ^2 + vot+so
Solve for the acceleration, a, in terms of the other variables. For this assessment item, you can use^to show exponent
and type your answer in the answer box, or you may choose to write your answer on paper and upload it.
Answer:
[tex]a=\frac{2S -2v_ot-2s_o}{t^2}[/tex]
Step-by-step explanation:
We have the equation of the position of the object
[tex]S = \frac{1}{2}at ^2 + v_ot+s_o[/tex]
We need to solve the equation for the variable a
[tex]S = \frac{1}{2}at ^2 + v_ot+s_o[/tex]
Subtract [tex]s_0[/tex] and [tex]v_0t[/tex] on both sides of the equality
[tex]S -v_ot-s_o = \frac{1}{2}at ^2 + v_ot+s_o - v_ot- s_o[/tex]
[tex]S -v_ot-s_o = \frac{1}{2}at ^2[/tex]
multiply by 2 on both sides of equality
[tex]2S -2v_ot-2s_o = 2*\frac{1}{2}at ^2[/tex]
[tex]2S -2v_ot-2s_o =at ^2[/tex]
Divide between [tex]t ^ 2[/tex] on both sides of the equation
[tex]\frac{2S -2v_ot-2s_o}{t^2} =a\frac{t^2}{t^2}[/tex]
Finally
[tex]a=\frac{2S -2v_ot-2s_o}{t^2}[/tex]
Two lines intersect at a:
• A. ray
• B. line
• C. point
• D. plane
Shawn has 25 coins, all nickels and dimes. The total value is $2.00. How many of each coin does he have?
Answer:
D=15 so N=10
Step-by-step explanation:
N+D=25 where the coins make up the number of nickels, N and the number of dimes, N
Now each nickel is worth .05 (not .5)
Each time is worth .10 or .1
So the two equations are .05N+.1D=2 and N+D=25
I'm going to multiply 100 on both sides so I can clear the decimals from first equation giving me 5N+10D=200.
So I'm going to multiply the second by 5 giving my 5N+5D=125
Line up equations and you should see we can solve this system by elmination by subtracting the equations
5N+10D=200
5N+5D=125
------------------
5D=75
D=75/5=15
So N+D=25 and D=15 so N=10.
Find the volume of a cone that has a radius of 9 and a height of 13.
Answer:
[tex]351 \pi[/tex] (about 1102.69902)
Step-by-step explanation:
The volume of a cone is represented by the formula [tex]V=\pi r^2 \frac{h}{3}[/tex], where [tex]V[/tex] is the volume, [tex]r[/tex] is the radius, and [tex]h[/tex] is the height.
Substitute in the values. [tex]V=\pi * 9^2 * \frac{13}{3}[/tex]Simplify the exponent. [tex]V=\pi * 81 * \frac{13}{3}[/tex]Multiply. [tex]V=351 \pi[/tex]This is as simple as the solution can get without estimating, but we can estimate with a calculator. [tex]351 \pi[/tex] is approximately equal to 1102.69902.
Answer is provided in the image attached.
... the product of the width and the height...
O A. won
B. h =
w
O c. wch
D. W:h
0
E. h-w
0
O
F. w+h
Step-by-step explanation:
The product of a and b is equal to a · b.
Let w - width and l - length, then the product of the width and the lenght is
w · h = wh
The product of width(w) and height(h) is equal to w.h.
What is the area?
The area is the sum of the areas of all its faces.The areas of the base, top, and lateral surfaces i.e all sides of the object. It is measured using different area formulas and measured in square units and then adding all the areas. The area of an object is a measure of the area that the surface of the object covers.
Let ;
w - width
l - length
∴ the product of the width and the length is w · h = wh
Learn more about the area here:-https://brainly.com/question/25292087
#SPJ2
Two bonds funds pay interest at rates of 3% Money invested for one year in the first fund earns $360 interest. The same amount invested in the other fund earns $480. find the lower rate of interest.
a = interest rate for first bond.
b = interest rate for second bond.
we know the rates add up to 3%, so a + b = 3.
we also know that investing the same amount hmm say $X gives us the amounts of 360 and 480 respectively.
let's recall that to get a percentage of something we simply [tex]\bf \begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}[/tex]
so then, "a percent" of X is just (a/100)X = 360.
and "b percent" of X is just (b/100)X = 480.
[tex]\bf a+b=3\qquad \implies \qquad \boxed{b}=3-a~\hfill \begin{cases} \left( \frac{a}{100} \right)X=360\\\\ \left( \frac{b}{100} \right)X=480 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \left( \cfrac{a}{100} \right)X=360\implies X=\cfrac{360}{~~\frac{a}{100}~~}\implies X=\cfrac{36000}{a} \\\\\\ \left( \cfrac{b}{100} \right)X=480\implies X=\cfrac{480}{~~\frac{b}{100}~~}\implies X=\cfrac{48000}{b} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf X=X\qquad thus\qquad \implies \cfrac{36000}{a}=\cfrac{48000}{b}\implies \cfrac{36000}{a}=\cfrac{48000}{\boxed{3-a}} \\\\\\ (3-a)36000=48000a\implies \cfrac{3-a}{a}=\cfrac{48000}{36000}\implies \cfrac{3-a}{a}=\cfrac{4}{3} \\\\\\ 9-3a=4a\implies 9=7a\implies \cfrac{9}{7}=a\implies 1\frac{2}{7}=a\implies \stackrel{\mathbb{LOWER~RATE}}{\blacktriangleright 1.29\approx a \blacktriangleleft}[/tex]
[tex]\bf \stackrel{\textit{since we know that}}{b=3-a}\implies b=3-\cfrac{9}{7}\implies b=\cfrac{12}{7}\implies b=1\frac{5}{7}\implies \blacktriangleright b \approx 1.71 \blacktriangleleft[/tex]
Manuela solved the equation below.
What is the solution to Manuela’s equation?
For this case we have the following equation:
[tex]2 (x + 2) = x-4[/tex]
Applying distributive property to the terms within the parentheses on the left side of the equation we have:
[tex]2x + 4 = x-4[/tex]
Subtracting "x" on both sides of the equation we have:
[tex]2x-x + 4 = -4\\x + 4 = -4[/tex]
Subtracting 4 on both sides of the equation we have:
[tex]x = -4-4\\x = -8[/tex]
Answer:
[tex]x = -8[/tex]
Answer:
x = -8
Step-by-step explanation:
We are given that Manuela solved following equation and we are to find its solution:
[tex] 2 ( x + 2 ) = x - 4 [/tex]
Expanding the left side of the equation by multiplying the terms inside the bracket by 2:
[tex]2x+4=x-4[/tex]
Arranging the equation in a way such that like terms are on each side (variables on the left and constants on the right):
[tex]2x-x=-4-4[/tex]
x = -8
Which best describes the transformation?
A. The transformation was a 90° rotation about the origin.
B. The transformation was a 180° rotation about the origin.
C. The transformation was a 270° rotation about the origin.
D. The transformation was a 360° rotation about the origin.
Answer:
Correct answer is "A"
Step-by-step explanation:
It is a tranformation about 90° in anti-clock wise direction
In geometry, transformations are used to move a point or points from one position to another. The transformation of [tex](x,y) \to (-y,x)[/tex] is a 90 degrees rotation about the origin.
Given that:
[tex]A(-1,1) \to A'(-1,-1)[/tex]
[tex]B(1,1) \to B'(-1,1)[/tex]
[tex]C(1,4) \to C'(-4,1)[/tex]
The transformation rule is:
[tex](x,y) \to (-y,x)[/tex]
When a point is rotated through [tex](x,y) \to (-y,x)[/tex]
Such point has undergone a 90 degrees counterclockwise rotation.
Hence, option (a) is correct.
Read more about transformation at:
https://brainly.com/question/19865582
Rewrite the equation by completing the square. x^2 +11 x +24 = 0
Answer:
[tex]\large\boxed{x^2+11x+24=0\Rightarrow(x+5.5)^2=6.25}[/tex]
Step-by-step explanation:
[tex](a+b)^2=a^2+2ab+b^2\qquad(*)\\\\x^2+11x+24=0\qquad\text{subtract 24 from both sides}\\\\x^2+(2)(x)(5.5)=-24\qquad\text{add}\ 5.5^2\ \text{to both sides}\\\\\underbrace{x^2+(2)(x)(5.5)+5.5^2}_{(*)}=-24+5.5^2\\\\(x+5.5)^2=-24+30.25\\\\(x+5.5)^2=6.25\Rightarrow x+5.5=\pm\sqrt{6.25}\\\\x+5.5=-2.5\ \vee\ x+5.5=2.5\qquad\text{subtract 5.5 from both sides}\\\\x=-8\ \vee\ x=-3[/tex]
To rewrite x^2 + 11x + 24 = 0 by completing the square, we first organize terms, then add the square of half the coefficient of x to both sides to create a perfect square. Taking the square root of both sides then provides the solution for x, resulting in x = -5.5 ± √6.25.
Explanation:To rewrite the equation x^2 + 11x + 24 = 0 by completing the square, we first need to make the quadratic and linear terms to create a square.
1. Rewrite the equation as: x^2 + 11x + __ = -24 + __
2. Take half of the coefficient of x, (11/2) and square it. (11/2)^2 = 30.25
3. Add this value on both sides of the equation:
x^2 + 11x + 30.25 = -24 + 30.25
4. Now, the left side of the equation is a perfect square and it can be written as:
(x + 5.5)^2 = 6.25
5. Finally, to solve for x, take the square root of both sides to get:
x + 5.5 = ± √6.25
x = -5.5 ± √6.25
Learn more about Completing the Square here:https://brainly.com/question/36246034
#SPJ2
The admission fee at an amusement park is $12, and each ride costs $3.50. The park also offers an all-day pass with unlimited rides for $33. For what numbers of rides is it cheaper to buy the all-day pass?
Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE = 11x -3 and CE = 12 - 4x. find x.
Answer: The value of x = 1
Step-by-step explanation:
Given : Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
[tex]AE = 11x -3 \text{ and} CE = 12- 4x.[/tex]
We know that the diagonal of a parallelogram bisects each other.
Therefore , we have the following equation :-
[tex]11x -3= 12- 4x\\\\\Righatrrow11x+4x=12+3\\\\\rightarrow\ 15x=15\\\\\Rightarrow\x=\dfrac{15}{15}=1[/tex]
Hence, the value of x = 1
if f(x)=-x^2+6x-1 and g(x)=3x^2-4x-1,find(f+g)(x)
Answer:
2x^2 +2x-2
Step-by-step explanation:
f(x)=-x^2+6x-1
g(x)=3x^2-4x-1
(f+g)(x)= -x^2+6x-1 +3x^2-4x-1
= 2x^2 +2x-2
what is the length of BC in the tight triangle below ?
Answer:
20
Step-by-step explanation:
use the Pythagorum therum (a^2+b^2=c^2
so you get 12^2+16^2=C^2
so that Equtes to 144+256=C^2
400=c^2
so square 400 and you get 20
For this case we have that by definition, the Pythagorean theorem states that:
[tex]c = \sqrt {a ^ 2 + b ^ 2}[/tex]
Where:
c: It is the hypotenuse of the triangle
a, b: Are the legs
According to the figure, the hypotenuse is represented by BC, then:
[tex]BC = \sqrt {12 ^ 2 + 16 ^ 2}\\BC = \sqrt {144 + 256}\\BC = \sqrt {400}\\BC = 20[/tex]
Thus, the hypotenuse of the triangle is 20
ANswer:
Option D
Dimple gets paid $3,100 per month.she pays $930 a month for rent.what percent of her monthly pay goes to rent
Answer:
Its 30%
Step-by-step explanation:
I used guess and check.
(25%)
3100*.25 = 775
(30%)
3100*.3 = 930
Answer:
30%.
Step-by-step explanation:
It is the fraction 930/3100 multiplied by 100.
Percentage that is rent = (930 * 100 ) / 3100
= 30%.
find the volume (in terms of pi) of a sphere if it’s surface area of 400pi ft squared
[tex]\bf \textit{surface area of a sphere}\\\\ SA=4\pi r^2~~ \begin{cases} r=radius\\ \cline{1-1} SA=400\pi \end{cases}\implies 400\pi =4\pi r^2 \implies \cfrac{\stackrel{100}{~~\begin{matrix} 400\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~} }{~~\begin{matrix} 4\pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}=r^2 \\\\\\ 100=r^2\implies \sqrt{100}=r\implies 10=r \\\\[-0.35em] ~\dotfill[/tex]
[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \implies V=\cfrac{4\pi (10)^3}{3}\implies V=\cfrac{4000\pi }{3}\implies V\approx 4188.79[/tex]
If the variance of the ages of the people who attended a rock concert is 38, what is the standard deviation of the ages? Round your answer to two decimal places
Answer:
[tex]\sigma=6.16[/tex]
Step-by-step explanation:
By definition, the variance V of a population is defined as:
[tex]V = \sigma^2[/tex]
Where [tex]\sigma[/tex] is the standard deviation
We know that [tex]V = 38[/tex], then we can solve the equation for the standard deviation [tex]\sigma[/tex]
[tex]38 = \sigma^2[/tex]
[tex]\sigma^2=38[/tex]
[tex]\sigma=\sqrt{38}[/tex]
[tex]\sigma=6.16[/tex]
Finally the standard deviation is: [tex]\sigma=6.16[/tex]
Anyone please help!!!!!!!!!!!!
well, lateral area means only the area of the sides, namely just the four triangular faces.
[tex]\bf \textit{area of an equilateral triangle}\\\\ A=\cfrac{s^2\sqrt{3}}{4}~~ \begin{cases} s=sides\\ \cline{1-1} s=8 \end{cases}\implies A=\cfrac{8^2\sqrt{3}}{4}\implies A=16\sqrt{3} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{area of the 4 triangles}}{4(16\sqrt{3})}\implies 64\sqrt{3}[/tex]
A system of linear equations contains two equations with the same slope.
Select all of the correct statements.
I A. The system may have two solutions.
-
B. The system may have infinitely many solutions.
C. The system may have one solution.
O
D. The system may have no solution.
SUBMIT
Answer:
B. The system may have infinitely many solutions
D. The system may have no solution
Step-by-step explanation:
we know that
If a system of linear equations contains two equations with the same slope
then
we may have two cases
case 1) The two equations are identical, in this case we are going to have infinite solutions
case 2) The two equations have the same slope but different y-intercept, (parallel lines) in that case the system has no solution.
If function f is vertically stretched by a factor of 2 to give function g, which of the following functions represents function g?
f(x) = 3|x| + 5
A. g(x) = 6|x| + 10
B. g(x) = 3|x + 2| + 5
C. g(x) = 3|x| + 7
D. g(x) = 3|2x| + 5
Answer:
A. g(x) = 6|x| +10
Step-by-step explanation:
The parent function is given as:
f(x) = 3|x| + 5
Applying transformation:
function f is vertically stretched by a factor of 2 to give function g.
To stretch a function vertically we multiply the function by the factor:
2*f(x) = 2[3|x| + 5]
g(x) = 2*3|x| + 2*5
g(x) = 5|x| + 10
Answer: Option A.
Step-by-step explanation:
There are some transformations for a function f(x).
One of the transformations is:
If [tex]kf(x)[/tex] and [tex]k>1[/tex], then the function is stretched vertically by a factor of "k".
Therefore, if the function provided [tex]f(x) = 3|x| + 5[/tex] is vertically stretched by a factor or 2, then the transformation is the following:
[tex]2f(x)=g(x)=2(3|x| + 5)[/tex]
Applying Disitributive property to simplify, we get that the function g(x) is:
[tex]g(x)=6|x| +10[/tex]
2. Find the product (11x2 + 7x - 3)(-5x + 1).
-55x3 - 24x2 + 22x - 3
Answer:
The product is -55x³ - 24x² + 22x - 3
Step-by-step explanation:
* Lets revise how to find the product of trinomial and binomial
- If (ax² ± bx ± c) and (dx ± e) are two binomials, where a , b , c , d , e
are constant, their product is:
# Multiply (ax²) by (dx) ⇒ 1st term in the trinomial and 1st term in the
binomial
# Multiply (ax²) by (e) ⇒ 1st term in the trinomial and 2nd term in
the binomial
# Multiply (bx) by (dx) ⇒ 2nd term the trinomial and 1st term in
the binomial
# Multiply (bx) by (e) ⇒ 2nd term in the trinomial and 2nd term in
the binomial
# Multiply (c) by (dx) ⇒ 3rd term in the trinomial and 1st term in
the binomial
# Multiply (c) by (e) ⇒ 3rd term the trinomial and 2nd term in
the binomial
# (ax² ± bx ± c)(dx ± e) = adx³ ± aex² ± bdx² ± bex ± cdx ± ce
- Add the terms aex² and bdx² because they are like terms
- Add the terms bex and cdx because they are like terms
* Now lets solve the problem
- There are a trinomial and a binomials (11x² + 7x - 3) and (-5x + 1)
- We can find their product by the way above
∵ (11x²)(-5x) = -55x³ ⇒ 1st term in the trinomial and 1st term in the binomial
∵ (11x²)(1) = 11x² ⇒ 1st term in the trinomial and 2nd term in the binomial
∵ (7x)(-5x) = -35x² ⇒ 2nd term the trinomial and 1st term in the binomial
∵ (7x)(1) = 7x ⇒ 2nd term in the trinomial and 2nd term in the binomial
∵ (-3)(-5x) = 15x ⇒ 3rd term in the trinomial and 1st term in the binomial
∵ (-3)(1) = -3 ⇒ 3rd term the trinomial and 2nd term in the binomial
∴ (11x² + 7x - 3)(-5x + 1) = -55x³ + 11x² - 35x² + 7x + 15x - 3
- Add the like terms ⇒ 11x² - 35x² = -24x²
- Add the like terms ⇒ 7x + 15x = 22x
∴ The product is -55x³ - 24x² + 22x - 3
PLEASE HELP! TRIG! Find the area of the triangles
Answer:
47.91 units²
Step-by-step explanation:
This can be solved using Heron's triangle (see attached)
in this case, your lengths are
a = 3+9=12
b=3+5=8
c=5+9=14
Hence,.
S = (1/2) x (a + b + c) = (1/2) (12+8+14) = 17
(s - a) = 17 -12 = 5
(s - b) = 9
(s - c) = 3
Area = √ [ s (s-a) (s-b) (s-c) ]
= √ [ 17 x 5 x 9 x 3 ] = √2295 = 47.9061 = 47.91 units² (rounded to nearest hundreth)
What is the change that occurs to the parent function f(x) = x2 given the function f(x) = x2 + 7.
ANSWER
shifts up 7 units.
EXPLANATION
The given function is
[tex]f(x) = {x}^{2} [/tex]
This is the base of the quadratic function without any transformation.
It is also refer to as the parent function.
The transformed function has equation:
[tex]f(x) = {x}^{2} + 7[/tex]
This transformation is of the form
[tex]y = f(x) + k[/tex]
This transformation shifts the graph of the base function up by k units.
Since k=7, the base function is shifted up by 7 units.
2. Find the value of x to the nearest tenth.
a. 4.5
b. 5.4
c. 6.3
d. 7.2
3. Find the value of x.
a. 7
b. 7.5
c. 8
d. 8.5
4. FG ⊥ OP, RS ⊥ OQ. FG=40, RS=40, OP=15. Find x.
a. 15
b. 17
c. 20
d. 21
5. Find the value of x to the nearest tenth.
a. 7.5
b. 7.9
c. 8.1
d. 8.9
Answer:
Part 2) Option b. 5.4
Part 3) Option c. 8
Part 4) Option a. 15
Part 5) Option d. 8.9
Step-by-step explanation:
Part 2) Find the value of x to the nearest tenth
we know that
x is the radius of the circle
Applying the Pythagoras Theorem
[tex]x^{2}=3.6^{2}+(8/2)^{2}[/tex]
[tex]x^{2}=28.96[/tex]
[tex]x=5.4\ units[/tex]
Part 3) Find the value of x
In this problem
x=8
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
Applying the Pythagoras Theorem
[tex]r^{2}=8^{2}+(15/2)^{2}[/tex]
[tex]r^{2}=120.25[/tex]
[tex]r=\sqrt{120.25}[/tex]
step 2
Find the value of x
Applying the Pythagoras Theorem
[tex]r^{2}=x^{2}+(15/2)^{2}[/tex]
substitute
[tex]120.25=x^{2}+56.25[/tex]
[tex]x^{2}=120.25-56.25[/tex]
[tex]x^{2}=64[/tex]
[tex]x=8\ units[/tex]
Part 4) Find the value of x
In this problem
x=OP=15
Verify
step 1
Find the radius of the circle
Let
r -----> the radius of the circle
In the right triangle FPO
Applying the Pythagoras Theorem
[tex]r^{2}=15^{2}+(40/2)^{2}[/tex]
[tex]r^{2}=625[/tex]
[tex]r=25[/tex]
step 2
Find the value of x
In the right triangle RQO
Applying the Pythagoras Theorem
[tex]25^{2}=x^{2}+(40/2)^{2}[/tex]
[tex]625=x^{2}+400[/tex]
[tex]x^{2}=625-400[/tex]
[tex]x^{2}=225[/tex]
[tex]x=15\ units[/tex]
Part 5) Find the value of x
Applying the Pythagoras Theorem
[tex]6^{2}=4^{2}+(x/2)^{2}[/tex]
[tex]36=16+(x/2)^{2}[/tex]
[tex](x/2)^{2}=36-16[/tex]
[tex](x/2)^{2}=20[/tex]
[tex](x/2)=4.47[/tex]
[tex]x=8.9[/tex]
6,13,20,27 based on the pattern what are the next two terms
The pattern is plus 7
6 + 7 = 13
13 + 7 = 20
20 + 7 = 27
This means to find the next term you must add 7 to 27
27 + 7 = 34
To find the term after 34 add seven to that as well
34 + 7 = 41
so...
6, 13, 20, 27, 34, 41
Hope this helped!
~Just a girl in love with Shawn Mendes
The equation 3x2 = 6x – 9 has two real solutions
True
O False
Answer:
False
Step-by-step explanation:
We first write the equation in the form ax² + bx + c=0 which gives us:
3x² - 6x + 9=0
Given the quadratic formula,
x= [-b ±√(b²- 4ac)]/2a ,the discriminant proves whether the equation has real roots or not.
The discriminant, which is the value under the root sign, may either be positive, negative or zero.
Positive discriminant- the equation has two real roots
Negative discriminant- the equation has no real roots
Zero discriminant - The equation has two repeated roots.
In the provided equation, b²-4ac results into:
(-6)²- (4×3×9)
=36-108
= -72
The result is negative therefore the equation has no real solutions.
Answer: FALSE
Step-by-step explanation:
Rewrite the given equation in the form [tex]ax^2+bx+c=0[/tex], then:
[tex]3x^2 = 6x - 9\\3x^2-6x +9=0[/tex]
Now, we need to calculate the Discriminant with this formula:
[tex]D=b^2-4ac[/tex]
We can identify that:
[tex]a=3\\b=-6\\c=9[/tex]
Then, we only need to substitute these values into the formula:
[tex]D=(-6)^2-4(3)(9)[/tex]
[tex]D=-72[/tex]
Since [tex]D<0[/tex] the equation has no real solutions.